We compute the average \(\operatorname{\mathbf {\ell }}_2\)  and LPIPS distances based on a standardly trained VGG network using the code from [1]} for different corruptions from CIFAR-10-C. The results are shown in Fig. REF  (see also Table REF  in the Appendix), where we observe that for certain corruptions, LPIPS clearly demonstrates a more preferable behavior than the \(\operatorname{\mathbf {\ell }}_2\)  distance.
For example, the \(\operatorname{\mathbf {\ell }}_2\)  distances of elastic transformations are monotonically decreasing over the corruption severity which is the opposite of what we would expect from a suitable distance between images. At the same time, the LPIPS distance is first slightly decreasing and then increasing which is a better behavior compared to \(\operatorname{\mathbf {\ell }}_2\) .
Similarly, the \(\operatorname{\mathbf {\ell }}_2\)  distances for JPEG corruption appear to be roughly constant while they are noticeably increasing for LPIPS.
The LPIPS distances for the frost corruption start from a low value and then monotonically increase whereas the \(\operatorname{\mathbf {\ell }}_2\)  distances start from a very high value and then fail to be monotonic.
At the same time, LPIPS behavior is more unexpected on noise corruption where it shows a very fast increase for impulse, Gaussian, and shot noises.
